I used to use a Mavic threadless BB, on which the lockrings had a 45° chamfer, and which required that the ends of the BB shell had a matching chamfer. This was rock solid and lasted until riding through floodwater followed by neglect killed it. In practice it isn't absolutely necessary to get the chamfer put on the BB shell - tightening up a few times will develop enough of a chamfer for it to work. This will apply to any other threadless BBs with a similar inward-pointing taper (Stronglight did one too).
Any threadless BB that relies completely on widthways clamping with nothing to resist up/down movement other than the clamping pressure will be vulnerable to movement and consequent loosening.
For cheap, there are (or were) also cartridge BB with nylon press in cups.
Buying now, I'd probably get the Velo Orange expanding version.
For a permanent fix, I had the BB threads in a frame replaced by Argos using the ream and sleeve method mentioned above. This has given no problems in the 15 years or so since.
Other framebuilders may also repair BB threads by either building up with braze and then threading the braze (I personally wouldn't trust this long term), or by cutting a saw slot through the BB shell, squeezeing the slot shut and brazing/welding it, then recutting the threads in the now slighly smaller diameter BB shell.